I also lightly wiped the metal parts since I knew they'd get touched at the edges anyway so I wanted to even them out.

I went over the entire gun twice, including opening the trapdoor and lightly swapping inside it where I saw clumps of the stuff that reminds me of cosmoline.

Then I went over it all one time with a dry rag.

Results:

The gun looks the same, but lots of brown stuff came off on the rags. Uniform, light or medium brown - looks more like oil than dirt, to me. It was coming off the wood. Some small amounts may have also come off the metal, but it reliably came off any time I polished the wood.

The stock may still be a little damp, so it's possible it will look a little lighter than before after fully drying.

I'll check again soon and make sure the metal is all dry. It was when I finished wiping it down, but some moisture could get back on it from the wood.

My belief is that the gun is dark mostly because somebody put unnecessary coats of oil on the gun after the linseed oil had already polymerized. But I might be wrong, this is the oldest stock I've ever tried to clean.